Statistics and the 2012 Presidential Election
Yes, I’ve been following the “horse race” very closely and think that I have some stuff that I can use to explain things to students.
For one: have studied “confidence intervals” and “hypothesis testing”. Nate Silver’s recent article has some examples of these:

First of all: what are these?

Each one of these is a so-called “90 percent confidence interval” that shows “Obama’s true support” in these states (or Congressional districts, in the case of NE-2 and ME-2).
What this means: we are 90 percent certain that Obama’s true support falls somewhere in this interval. Example: in New Mexico, Obama’s lead is 2.3 to 15.5. In Montana, Romney’s lead is between 2.2 and 17.1.

Note: the widths of these intervals are a bit different; that is because the respective distributions have different “standard deviations” and the higher the number of people polled, the smaller the standard deviation. A 90 percent confidence interval is about plus/minus 1.645 standard deviations.

Now note that each interval is colored blue, red or mixed. An “all blue” band means that we are 90 percent sure that President Obama leads in that region. An “all red” means that we are 90 percent sure that Governor Romney leads. If a band is mixed color (Wisconsin to North Carolina (mostly)) that means that we do NOT have 90 percent confidence that Mr. Obama or Mr. Romney leads.

This is an example of “hypothesis testing”; if a band is all blue we reject the “null hypothesis” that the race is tied and conclude that one candidate is ahead with 90 percent confidence.

However, unless the dividing line of the colors is right in the middle of the band, we can make a probability estimate of who is ahead.
Let’s look at Wisconsin. We see just a tip of red there and a number that says 88 percent. What this means: if we were willing to settle for being 88 percent confident, we could concluded that Obama was ahead there. In North Carolina, if we wanted to settle for 81 percent confidence, we’d conclude that Romney was ahead.

Now write these percentages as decimals and subtract them from 1. That is called “the p-value”. For Wisconsin: we’d have 1-.88 = .12 and we’d say “P = .12” for a “one-tailed test”.
For North Carolina: 1-.81 = .19 so we’d say P = .19.

Predicted values versus expected values
Nate Silver also says this:

Mr. Obama is not a sure thing, by any means. It is a close race. His chances of holding onto his Electoral College lead and converting it into another term are equivalent to the chances of an N.F.L. team winning when it leads by a field goal with three minutes left to play in the fourth quarter. There are plenty of things that could go wrong, and sometimes they will.

But it turns out that an N.F.L. team that leads by a field goal with three minutes left to go winds up winning the game 79 percent of the time. Those were Mr. Obama’s chances in the FiveThirtyEight forecast as of Wednesday: 79 percent.

First about that NFL stat: if that sounds strange, let’s remember that the 79 percent is the probability that the team that is down by 3 with first and 10 at its own 20 with 3 minutes to go in the game loses the game. That doesn’t mean “never catches up”; they could catch up, and even go ahead and still lose the game. This is “total probability of losing the game.

That puts it into some perspective. The reason: we are trying to predict the outcome of THIS single election. That is a “predictive value” problem.

Now if we were having this election in, say, 1000 parallel universes with roughly the same conditions, Obama would win close to 80 percent of such elections. This would be an “expected value”: the percentage of Obama wins over a large number of cases with similar conditions.

So if the election were decided by a “majority of election outcomes over a large number of trials”, well, this election WOULD be over and THAT would be an “expected value” problem.
But this election is valid on this universe only, and that is a predictive value problem. Hence BOTH campaigns are sweating at the moment.

About Blueollie

To keep track of my sports activities. I rarely train for anything anymore; mostly I just do workouts of the following types: running, walking, weight lifting and swimming. My best ultra accomplishment was walking 101 miles in 24 hours in 2004. These days, I walk a marathon every once in a while (5:50 to 7 hours) There was a time when I could run a sub 40 minute 10K (did that once), but that was another lifetime ago; these a days 2427-2825 25:50-27:45 minutes for a 5K would be more like it. I also have an off and on interest in yoga and in weight training. My lifetime PB in the bench is 310; currently I do sets of 4-5 with 190.

To discuss the football, basketball or baseball game I’ve been to. Since 2011, I started to attend live football games regularly (University of Illinois, sometimes Illinois State, sometimes either the Colts or Bears of the NFL…don’t get me started on the Rams) ; I’ve attended Bradley Basketball games (men and women) for some time. In the past 3 years, I started to watch live baseball again (mostly the Peoria Chiefs and Bradley University).

From time to time, I post what I am thinking about mathematically

I often post links to science articles, especially articles about cosmology and evolution.

I am very sympathetic to the “new atheist” movement, though some might consider me to be an agnostic. I reject any notion of a deity that interferes with physical events, but remain agnostic to the idea that there might be something “grand and wonderful” (Dawkins’ phrase) outside of our current spacetime continuum.

I am a liberal Democrat who thinks that the current social atmosphere is tilted way too far toward the interests of big business, and I reject the idea that a “free market” cures all ills, though pure socialism doesn’t work either. I am also a believer in the freedom of speech, including speech that I might not like. Also, I’ve been involved (to a moderate degree) with political campaigns, ranging from City Council races up to Presidential races.

I like to post photos of trips and vacations.

I like women in spandex. 🙂

The 2016 election: I voted for Hillary Clinton and was dismayed that she lost the Electoral College, though I take a bit of comfort that a plurality of voters preferred her (by just over 2 percentage points!)

I see Donald Trump as an unqualified amateur who lacks the humility and deportment to be an effective president; I sure hope the time proves me wrong. I’ve been wrong before (e. g. my election prediction) and will be wrong again. I hope this is one of those times.